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Switching to Neovim is a rite of passage for many developers. It's not just about using a terminal editor; it's about crafting a Personalized Development Environment (PDE) that moves at the speed of thought. In this post, I'll walk you through my cur...
A P2P (peer-to-peer) network is like a group of friends where everyone shares and helps each other directly — there’s no boss or central person in charge. Instead of going to a central server (like a library or a big store), you go directly to anothe...
So far we covered: Group Law Fields and how field operations works Divisors Now in this part we will explore: Pairing Groups Expand on r-torsian groups Pairing types Twisted Curves Weil and Tate Pairings Pairing groups Let’s define biline...
In the previous part we explored Fields, Torsion Points, and Endomorphism. Now we are gonna take our understanding of the topic further and dig into more constructions revolving around the Elliptic Curves, namely: Divisors Overview of Principal div...
In this blog series we will be digging deep into the working of bilinear pairings in Elliptic curves over finite fields. The following series presumes you have a decent understanding Elliptic Curves: Group law - the chord and tangent rule. Fields a...
Welcome to a deep dive into Verkle trees and their impact on Ethereum's state management. As Ethereum aims to improve scalability and efficiency, Verkle trees are becoming a key part of the solution. In this blog, we'll break down what Verkle trees a...
Prerequisites: Understanding of what QAP is and how to create one from R1CS. Group theory understandings Bilinear Pairings Probabilistic Checkable Proofs ( PCP ) What is a PCP: Prover generates a PCP oracle, which can be thought of as a big mes...
In this article, we will explore how the following topics: R1CS Transcript Selector Polynomial Vanishing Polynomial Quadratic Arithmetic Program R1CS The term "R1CS" stands for "Rank-1 Constraint System." It's a method used in computer scienc...
The FRI (Fast Reed-Solomon Interactive Oracle) commitment scheme is a cryptographic protocol that plays a crucial role in various zero-knowledge proof systems. It's designed to efficiently prove the correctness of computations without revealing any u...